You are allowed to backup your Android device to your Google account and of course you can restore the backup files from your Google account back to Android phone. Then, how to restore your Android device from Google? Just be sure that your phone contacts are really synced with your Google account and Google will restore them automatically after you perform a device wipe. However, Google is unable to backup everything on your Android phone, let along allows you to manage your backup files. And if you don't have a Google account yet, you can't use this backup way.
Alternative way to backup & Restore your Android device:
Do you want a more convenient solution to backup overall file types from your Android phone or Android tablet? Then, I'd like to suggest you have a try with the Coolmuster Android Assistant or Coolmuster Android Assistant for Mac, which is regarded as the best Android mobile backup tool and plays an important role in backing up valuable Android data to PC or Mac computer. It allows you to backup almost everything from your Android devices, such as contacts, SMS, photos, videos, music, documents, eBooks, apps, etc., no matter on your Android internal or external memory card to computer with just a few clicks.
Restoring the backup files from computer to Android phone by using Coolmuster Android Assistant is also easy. What you need to do is just clicking on the "Restore" button, then, the backed up record will be synced back to your Android phone with one click. Just download the free demo version of the Android backup tool to have a try.
Tutorial to Restore Android Backup Files from Computer with Android Assistant
Step 1. Run the program and connect your Android device to computer
Once you have backed up your Android to computer by using this Coolmuster Android Assistant, you can follow the steps here to restore the backup record back to your Android phone with one click. Just launch the Android Assistant again and connect your Android phone to the computer.
Step 2: Start to restore Android phone from backup on computer
After the Android Assistant detects your Android phone, all file types on your Android device will be shown as Music, Videos, Photos, Contacts, Apps, Books, etc., along with several options like Export, Import, Restore, etc. Just choose the Restore button and the backup record on your computer will appear. Just choose the backup file you need and click OK to restore them to the connected Android phone.
See? Only with two steps, you can restore backup files to Android phone from computer successfully.